Question: Solve for $x$ and $y$ using substitution. ${-4x-5y = 3}$ ${x = 6y-8}$
Answer: Since $x$ has already been solved for, substitute $6y-8$ for $x$ in the first equation. ${-4}{(6y-8)}{- 5y = 3}$ Simplify and solve for $y$ $-24y+32 - 5y = 3$ $-29y+32 = 3$ $-29y+32{-32} = 3{-32}$ $-29y = -29$ $\dfrac{-29y}{{-29}} = \dfrac{-29}{{-29}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x = 6y-8}\thinspace$ to find $x$ ${x = 6}{(1)}{ - 8}$ $x = 6 - 8$ ${x = -2}$ You can also plug ${y = 1}$ into $\thinspace {-4x-5y = 3}\thinspace$ and get the same answer for $x$ : ${-4x - 5}{(1)}{= 3}$ ${x = -2}$